Edexcel A Level Maths: Pure:复习笔记2.1.2 Manipulating Surds
Manipulating Surds
What are surds?
- If n is a positive integer and is not a square number, then √n (or any multiple of √n ) is a surd
- Surds are examples of irrational numbers
What do I need to know about manipulating surds?
- There are two basic rules you need to know in order to manipulate and simplify surds:
- When simplifying, look for square factors
- You can collect like terms with surds like you do with letters in algebra:
- But be careful not to confuse this with the multiplication and division rules... cannot add or subtract 'under the surd':
Where can surds be useful?
- Using surds lets you leave answers in exact form
- e.g.
rather than
- e.g.
- Understanding how to simplify surds can help reduce expressions and collect like terms
Exam Tip
- Leaving answers in surd form can be really helpful when you need to carry an exact value through to another part of working
- When simplifying surds, remembering your square numbers is really helpful!
Worked Example
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